The correct order of acid strength of the following carboxylic acids is -

Statement 1 The geometrical isomer of the complex \(\left.\left[\mathrm{M}_{\left(\mathrm{NH}_3\right.}\right)_4 \mathrm{Cl}_2\right]\) are optically inactive.
Statement 2 Both geometrical isomers of the complex \(\left[\mathrm{M}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]\) possess axis of symmetry.

The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

Dissolving \(120 \mathrm{~g}\) of urea (molecular weight 60) in \(1000 \mathrm{~g}\) of water gave a solution of density \(1.15 \mathrm{~g} / \mathrm{mL}\). The molarity of the solution is

A positron is emitted from \({ }_{11}^{23} \mathrm{Na}\). The ratio of the atomic mass and atomic number of the resulting nuclide is

Match the gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of \(4 \times 4\) matrix given in the ORS.

Column I	Column II
A. Hydrogen gas \((P=200 atm,\) \(T=273 K)\)	p. Compressibility factor \(\neq 1\)
B. Hydrogen gas \((P \sim 0,\) \(T=273 K)\)	q. Attractive forces are dominant
C. \(CO _2(P=1 atm,\) \(T=273 K)\)	r. \(P V=n R T\)
D. Real gas with very large molar volume	s. \(P(V-n b)=n R T\)

List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List-I.

List-I	List-II
(I)	$\left(\mathrm{P}\right)$
(II)	$\left(\mathrm{Q}\right)$
(III)	$\left(\mathrm{R}\right)$
(IV)	$\left(\mathrm{S}\right)$
	$\left(\mathrm{T}\right)$
	$\left(\mathrm{U}\right)$

Which of the following options has correct combination considering List-I and List-II?

Paragraph :
When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Question :
If \(r=5 \times 10^{-4} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\), \(g=10 \mathrm{~ms}^{-2}, T=0.11 \mathrm{Nm}^{-1}\), the radius of the drop when it detaches from the dropper is approximately

The figure shows the \(p-V\) plot of an ideal gas taken through a cycle \(A B C D A\). The part \(A B C\) is a semi-circle and \(C D A\) is half of an ellipse. Then,

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

A parallel plate capacitor having plates of area $\mathrm{S}$ and plate separation $\mathrm{d}$ , has capacitance ${\mathrm{C}}_1$ in air. When two dielectrics of different relative permittivities ( ${\mathrm{\epsilon }}_1=2\mathrm{}$ and ${\mathrm{\epsilon }}_2=4$ ) are introduced between the two plates as shown in the figure, the capacitance becomes ${\mathrm{C}}_2$ . The ratio $\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1}$ is

Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 16& 4& 1\end{array}\right]$ and $I$ be the identity matrix of order $3$. If $Q=\left[q_{ij}\right]$ is a matrix such that $P^{50}-Q=I,$ then the value of $\frac{q_{31}+q_{32}}{q_{21}}$ is equal to

The increasing order of atomic radii of the following group $13$ elements is